Geodesic
The Fractal Dimension of Sets Derived from Complex Bases
Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 495-500

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For each positive integer n, the radix representation of the complex numbers in the base —n + i gives rise to a tiling of the plane. Each tile consists of all the complex numbers representable in the base -n + i with a fixed integer part. We show that the fractal dimension of the boundary of each tile is 2 log λn/log(n2 + 1), where λn is the positive root of λ3 - (2n - 1) λ2 - (n - 1) 2λ - (n2 + 1).
DOI : 10.4153/CMB-1986-078-1
Mots-clés : 11K55, 51M20 
Gilbert, William J. The Fractal Dimension of Sets Derived from Complex Bases. Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 495-500. doi: 10.4153/CMB-1986-078-1
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     author = {Gilbert, William J.},
     title = {The {Fractal} {Dimension} of {Sets} {Derived} from {Complex} {Bases}},
     journal = {Canadian mathematical bulletin},
     pages = {495--500},
     year = {1986},
     volume = {29},
     number = {4},
     doi = {10.4153/CMB-1986-078-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-078-1/}
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